Despite the lack of support to swap in different hard drives (especially ones of a larger capacity) in the Xbox One, this guy says he's gotten the two pieces of hardware to cooperate. Not only that, the console runs faster with a non-stock hard drive installed.
Booting to the main screen goes about 10 per cent faster with one; loading a level in Call of Duty: Ghosts goes about 20 per cent faster.
Of course, installing this drive (or any) is going to void your warranty. And, as he points out, he still needs to figure out how to partition the drive so that its full capacity can be used. But the video suggests it can be done, at least.
As for why the Xbox One wouldn't support such modifications, that should be obvious. Christ, they won't even expose how much space you're using on the OEM drive. You sell a lot more peripherals and create a lot more demand for future models this way. I can't upgrade the hard drive in my iPad 4 for example, which for some reason needs 1.2GB of hard drive space to implement a 50MB operating system update. Oh noes! I should buy a new machine rather than delete games from the old one.